Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > bitr3i | Structured version Visualization version GIF version |
Description: An inference from transitive law for logical equivalence. (Contributed by NM, 2-Jun-1993.) |
Ref | Expression |
---|---|
bitr3i.1 | ⊢ (𝜓 ↔ 𝜑) |
bitr3i.2 | ⊢ (𝜓 ↔ 𝜒) |
Ref | Expression |
---|---|
bitr3i | ⊢ (𝜑 ↔ 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bitr3i.1 | . . 3 ⊢ (𝜓 ↔ 𝜑) | |
2 | 1 | bicomi 227 | . 2 ⊢ (𝜑 ↔ 𝜓) |
3 | bitr3i.2 | . 2 ⊢ (𝜓 ↔ 𝜒) | |
4 | 2, 3 | bitri 278 | 1 ⊢ (𝜑 ↔ 𝜒) |
Copyright terms: Public domain | W3C validator |